You should do your home work and, [if you have more extra time, you
should also prepare for exams].
Preliminary point: the commas are optional not obligatory.
The bracketed bit is a conditional construction where the clause that is complement of if is the protasis (the condition) followed by the apodosis (the outcome of the condition being met).
The if ...
Assuming that what's inside the comma pairs is parenthetical, then it's grammatical status is debatable, but its conventional use is wrong because of the punctuation.
When analyzing a sentence, do so by removing the parenthetical information. In the specific example here, the following is the result:
You should do your home work, and if you have more ...
"being" is the verb(-ing) of your 2nd clause. You can separate the sentence into 2 as follows:
Major refreshes to the OS come about every six months. The most recent one is the May 2019 Update.
You can add a noun (mainly the subject) between "recent" and "being". For example:
..., with the most recent refresh being the May 2019 update
However, that ...
The sentence is missing something that defines the causal relationship between "the accelerating decline of sales" and "compact discs would not be compensated [...]"
You could say as suggested:
The music company was afraid that the accelerating decline of sales of compact discs would not be compensated by increased internet revenue.
Or some others:
The sentence is equivalent to
I wish I could write English with more freedom than the amount of freedom which is at present possible.
Than can be followed by a clause with or without a subject. The implied object of comparison may take different roles in that clause:
There was more food than I wanted. (object of "I wanted")
It seems that there ...